| Sample Asset Portfolio | |||
|---|---|---|---|
| instrument | face_value | coupon_rate | maturity |
| $15M UST 1Y | $15,000,000 | 3.68% | 1 |
| $10M UST 1Y | $10,000,000 | 3.49% | 1 |
| $25M UST 7Y | $25,000,000 | 3.98% | 7 |
| $15M Corp A 5Y | $15,000,000 | 4.25% | 5 |
| $10M PC BB 20Y | $10,000,000 | 10.50% | 20 |
UA ALM 20260210
1. Introduction
Brennen Slaney
Personal Background
- Grew up in Cincinnati, OH
- Family is from Pittsburgh, huge Steelers fan
- Have lived in Nashville, TN since graduating
- Love to travel, run, lift, catch up with friends and try new restuarants
Education
- Attended the University of Alabama from 2016-2019
- Bachelors in Finance
- Masters in Applied Statistics
Career
Cigna
- Started off as a health actuary in Cigna’s Nashville office as a part of the Actuarial Executive Development Program
Medicare Pricing
- Lots of excel based models that broke easily
- Long hours, all plans for the year were due first Monday in June, very stressful
- Learned a lot about Excel, VBA and how government funded health insurance worked
Pharmacy Trend
- Various tools (Excel, R, SQL, Python) and business partners (formulary, FP&A, pricing, underwriting, clinical)
- Learned how complicated the Rx ecosystem was, many layers and no pricing was straightforward
- Responsible for a lot of actuarial-judgment on current events, like projecting GLP-1 drug trends in early 2023, or modeling out what financials would be when the COVID emergency status ended
Fortitude Re
- After 3 years, switched to Life & Annuity Reinsurance
- Much more asset exposure, long term products
- Finished final FSA exam in health, began taking CFA exams to learn the asset side of the business
- You are not stuck in the sector you start in out of college!!
Experience Studies
- Intersection of data science and actuarial
- Used Python and GitHub to build internal package called HEAT to handle repeatable tasks in an Experience Study
- Reformatted studies to modern technology, and present results to Actuarial leaders to inform assumption updates
Planning & Strategy
- Learning and applying a lot of the ALM concepts presented today!
- Run Quarterly SBA ALM Model using inputs from actuarial modeling, investment analytics and capital management. We own the modeling and reinvestment to keep ALM principles in line throughout the projection
- Produce daily hedge targets using an automated Python script that runs each night to attribute daily changes to different data updates
- Investments ALM team uses our hedge targets to understand duration and convexity shifts in liabilities overnight, compare to assets, and place swap trades as needed to keep duration within threshold
Credentials
- ASA in 2022
- FSA in 2024
- Passed CFA Levels I and II, taking III in August
2. Building Blocks of ALM
How are assets and liabilities measured, and why do actuaries care?
Assets
Assets are the money you have. Most of it is invested in safe, predictable instruments:
- Treasuries
- Highly rated corporate bonds
- Mortgage-Backed Securities
- Not much Bitcoin
The goal is positive expected yield with lower variance. Regulators enforce capital requirements and “score” the safety of assets. Investment teams manage the portfolio, but actuaries are often involved.
For this presentation we’ll use the following sample portfolio:
Liabilities
Liabilities are money you owe. Nearly every insurance contract comes with a liability for the insurer. The timing and amount can be known or unknown:
- Known — Annuity Certain (fixed schedule of payments)
- Unknown — Term Life (death benefit contingent on mortality)
Actuaries are the liability experts!
| Liability Summary | |||||
|---|---|---|---|---|---|
| product | amount | amount_label | premium | premium_label | age |
| Whole Life | $1,000,000 | face value | $9,730 | annual | 40 |
| SPIA | $120,000 | annual payout | $1,734,014 | single | 65 |
Equity
Equity = Assets - Liabilities
- Without equity, a company will be liquidated by regulators
- Stability is important — you don’t want drastic swings
- Excess capital funds expansion, retained earnings, and dividends
- When you buy a stock, you are taking a stake in their equity. $0 Equity = $0 Stock Price
Example
If Assets = $100M and Liabilities = $80M, then Equity = $20M. That $20M funds new projects, dividends, bonuses, regulatory requirements.
3. Cashflows from Assets and Liabilities
What do these things actually look like?
Asset Cashflows
| $25M UST 7Y — Cashflows (first 10 periods) | |||
|---|---|---|---|
| period | coupon | principal | total |
| 1 | $497,500 | $0 | $497,500 |
| 2 | $497,500 | $0 | $497,500 |
| 3 | $497,500 | $0 | $497,500 |
| 4 | $497,500 | $0 | $497,500 |
| 5 | $497,500 | $0 | $497,500 |
| 6 | $497,500 | $0 | $497,500 |
| 7 | $497,500 | $0 | $497,500 |
| 8 | $497,500 | $0 | $497,500 |
| 9 | $497,500 | $0 | $497,500 |
| 10 | $497,500 | $0 | $497,500 |
Liability Cashflows
| Whole Life — Expected Cashflows (first 24 periods) | |||||
|---|---|---|---|---|---|
| period | year | survival_prob | expected_premium | expected_benefit | net_cashflow |
| 1 | 0.083333 | 0.9999 | $811 | $80 | −$731 |
| 2 | 0.166667 | 0.9998 | $811 | $80 | −$731 |
| 3 | 0.25 | 0.9998 | $811 | $80 | −$731 |
| 4 | 0.333333 | 0.9997 | $811 | $80 | −$731 |
| 5 | 0.416667 | 0.9996 | $811 | $80 | −$731 |
| 6 | 0.5 | 0.9995 | $811 | $80 | −$731 |
| 7 | 0.583333 | 0.9994 | $810 | $80 | −$731 |
| 8 | 0.666667 | 0.9994 | $810 | $80 | −$731 |
| 9 | 0.75 | 0.9993 | $810 | $80 | −$731 |
| 10 | 0.833333 | 0.9992 | $810 | $80 | −$731 |
| 11 | 0.916667 | 0.9991 | $810 | $80 | −$731 |
| 12 | 1.0 | 0.9990 | $810 | $80 | −$731 |
| 13 | 1.083333 | 0.9990 | $810 | $86 | −$724 |
| 14 | 1.166667 | 0.9989 | $810 | $86 | −$724 |
| 15 | 1.25 | 0.9988 | $810 | $86 | −$724 |
| 16 | 1.333333 | 0.9987 | $810 | $86 | −$724 |
| 17 | 1.416667 | 0.9986 | $810 | $86 | −$724 |
| 18 | 1.5 | 0.9985 | $810 | $86 | −$724 |
| 19 | 1.583333 | 0.9984 | $810 | $86 | −$724 |
| 20 | 1.666667 | 0.9984 | $810 | $86 | −$724 |
| 21 | 1.75 | 0.9983 | $810 | $86 | −$724 |
| 22 | 1.833333 | 0.9982 | $809 | $86 | −$724 |
| 23 | 1.916667 | 0.9981 | $809 | $86 | −$724 |
| 24 | 2.0 | 0.9980 | $809 | $86 | −$724 |
| SPIA — Expected Cashflows (first 24 periods) | ||||
|---|---|---|---|---|
| period | year | payout | survival_prob | expected_payout |
| 1 | 0.083333 | $10,000 | 0.9994 | $9,994 |
| 2 | 0.166667 | $10,000 | 0.9989 | $9,989 |
| 3 | 0.25 | $10,000 | 0.9983 | $9,983 |
| 4 | 0.333333 | $10,000 | 0.9977 | $9,977 |
| 5 | 0.416667 | $10,000 | 0.9972 | $9,972 |
| 6 | 0.5 | $10,000 | 0.9966 | $9,966 |
| 7 | 0.583333 | $10,000 | 0.9960 | $9,960 |
| 8 | 0.666667 | $10,000 | 0.9954 | $9,954 |
| 9 | 0.75 | $10,000 | 0.9949 | $9,949 |
| 10 | 0.833333 | $10,000 | 0.9943 | $9,943 |
| 11 | 0.916667 | $10,000 | 0.9937 | $9,937 |
| 12 | 1.0 | $10,000 | 0.9932 | $9,932 |
| 13 | 1.083333 | $10,000 | 0.9926 | $9,926 |
| 14 | 1.166667 | $10,000 | 0.9920 | $9,920 |
| 15 | 1.25 | $10,000 | 0.9914 | $9,914 |
| 16 | 1.333333 | $10,000 | 0.9908 | $9,908 |
| 17 | 1.416667 | $10,000 | 0.9902 | $9,902 |
| 18 | 1.5 | $10,000 | 0.9896 | $9,896 |
| 19 | 1.583333 | $10,000 | 0.9890 | $9,890 |
| 20 | 1.666667 | $10,000 | 0.9884 | $9,884 |
| 21 | 1.75 | $10,000 | 0.9877 | $9,877 |
| 22 | 1.833333 | $10,000 | 0.9871 | $9,871 |
| 23 | 1.916667 | $10,000 | 0.9865 | $9,865 |
| 24 | 2.0 | $10,000 | 0.9859 | $9,859 |
Equity (Surplus) View
| Balance Sheet — Present Values | |
|---|---|
| component | present_value |
| Assets | $83,932,581 |
| Liabilities | $1,734,014 |
| Surplus (Equity) | $82,198,568 |
That’s all there is to it — as long as interest rates never change again! Once we confirm that, we can go on a nice vacation and our work is done.
…okay, there’s more work to do.
4. Key Mathematical Concepts
Let’s measure interest rate risk.
Duration
Duration is the time-weighted average of the present value of cashflows. It measures a bond’s sensitivity to interest rate changes and helps us linearly estimate price changes from rate movements.
Convexity
Convexity captures the second-order (curvature) effect of yield changes on price. Using duration and convexity leads to better price-change estimates.
The second-order price approximation is:
DV01 (Dollar Value of a Basis Point)
The dollar change in value for a 1 bps parallel shift in the yield curve. This tells us how much money we expect our portfolio to move from a 1 bps shift.
| DV01 by Instrument | |
|---|---|
| instrument | dv01 |
| $15M UST 1Y | $1,453 |
| $10M UST 1Y | $967 |
| $25M UST 7Y | $15,122 |
| $15M Corp A 5Y | $6,781 |
| $10M PC BB 20Y | $21,474 |
Key Rate Duration (KRD)
The dollar change in value for a 1 bps shift at a specific duration on the yield curve. For example, KRD-7 measures the Dollar-Duration impact of a rate shift ONLY at year 7.
Key properties:
- KRDs across all tenors sum to the bond’s effective duration
- A bullet bond has KRD concentrated at its maturity
- An amortizing bond (e.g. mortgage) has KRD spread across many tenors
Immunization (Preview)
Redington Immunization Conditions
Immunization protects a portfolio’s ability to meet liabilities against interest rate movements:
- PV Match: PV(Assets) = PV(Liabilities)
- Duration Match: Duration(Assets) = Duration(Liabilities)
- Convexity Condition: Convexity(Assets) >= Convexity(Liabilities)
5. Revisit Cashflows with Rate Shocks
What happens when interest rates move?
| Present Values Under Rate Shocks | ||||
|---|---|---|---|---|
| rate_shock | discount_rate | pv_assets | pv_liabilities | surplus |
| -1% | 3.0% | $88,767,255 | $1,988,116 | $86,779,140 |
| +0% | 4.0% | $83,932,581 | $1,734,014 | $82,198,568 |
| +1% | 5.0% | $79,584,033 | $1,533,753 | $78,050,280 |
| +2% | 6.0% | $75,655,892 | $1,372,436 | $74,283,456 |
Key Observation
Notice how assets and liabilities respond differently to rate changes. This mismatch is the core problem ALM solves.
6. Duration Hedging with Swaps
Strategic Asset Allocation
Strategic Asset Allocation (SAA) determines how well assets and liabilities naturally hedge each other.
- Are our liabilities and assets of similar duration and convexity?
- Are they similarly sensitive to interest rates?
- If our bonds change in value similarly to our annuities, we have a natural ALM hedge
- If they respond differently, we need to actively stabilize the surplus
| Default SAA Weights | |
|---|---|
| asset_class | weight |
| govt_bonds | 40% |
| corp_bonds | 30% |
| mortgages | 20% |
| private_credit | 10% |
Interest Rate Swaps
A plain-vanilla interest rate swap exchanges fixed payments for floating payments. Swaps adjust portfolio duration without buying or selling bonds:
- Receive-fixed adds duration (like buying a bond)
- Pay-fixed removes duration (like selling a bond)
| Swap DV01 | ||
|---|---|---|
| swap | notional | dv01 |
| 5Y Receive-Fixed | $10,000,000 | $4,491 |
| 10Y Receive-Fixed | $10,000,000 | $8,176 |
Duration Gap Analysis
| Duration Gap Analysis | |
|---|---|
| component | dv01 |
| Assets | $45,797 |
| Liabilities | $2,242 |
| Gap (L - A) | −$43,555 |
7. Immunization
Immunization matches both duration and convexity to protect surplus against rate movements.
We solve a 2x2 system using two hedging instruments (e.g. a 5Y and 10Y swap):
where denotes dollar convexity.
| Gaps to Close | |
|---|---|
| metric | gap |
| Dollar Duration (DV01) | −$43,555 |
| Dollar Convexity | −$4,318,446,840 |
| Immunization Hedge Notionals | ||
|---|---|---|
| instrument | notional | direction |
| 5Y Swap | $5,808,930 | Receive-fixed |
| 10Y Swap | −$56,464,725 | Pay-fixed |
| Surplus: Unhedged vs Immunized | ||
|---|---|---|
| rate_shock | surplus_unhedged | surplus_hedged |
| -1% | $86,779,140 | $82,199,882 |
| +0% | $82,198,568 | $82,198,568 |
| +1% | $78,050,280 | $82,197,268 |
| +2% | $74,283,456 | $82,188,468 |
8. Conclusion
Key Takeaways
- Assets must be structured to meet liabilities under multiple rate scenarios
- Duration and convexity are the primary tools for measuring interest rate risk
- DV01 translates rate sensitivity into dollar terms at the portfolio level
- Immunization (matching duration + convexity) protects surplus from rate movements
- Strategic Asset Allocation and interest rate swaps are practical hedging tools
- Diversification across asset classes reduces mismatch risk
- Regular surplus monitoring is essential for actuarial compliance
Key ALM Strategies
| Strategy | Description |
|---|---|
| Immunization | Match duration and convexity of assets to liabilities to protect surplus |
| Cash Flow Matching | Structure asset cash flows to precisely meet liability payment schedules |
| Surplus Optimization | Maximize expected surplus return subject to risk constraints |
Questions & Discussion
Source code: github.com/realslimslaney/ALM